%%%%%%%%% \section{Table - Insurer Operating Results By Portfolio Size}
%%%%%%%%% \label{tab:InsurerOperatingResultsByPortfolioSize}
%\vspace{-1in}
\begin{table}[htbp]
%\vspace{-1in}
\caption{Maximum Sustainable Benefits (Ratio To Premiums) To Match PI's Probability Of Earning Profits (Avoiding Losses) By Portfolio Size} 
\begin{center}
\scalebox{0.8}{
\begin{tabular}{rrc|rrr|rr}
%\multicolumn{2}{c}{Genotype} & &
%\multicolumn{1}{c}{Dummy for additivity} &
%\multicolumn{1}{c}{Dummy for dominance }\\
%\multicolumn{1}{c}{Label} &    
%\multicolumn{1}{c}{Index i} &
%\multicolumn{1}{c}{Genotypic value ($\eta$)}&
%\multicolumn{1}{c}{effect $\alpha$ (x)} &
%\multicolumn{1}{c}{effect $\delta$ (z)}\\
\hline
\hline
& & & \multicolumn{3}{c}{Match PI's Profits} & \multicolumn{2}{|c}{Match PI's Loss Avoidance} \\
& & & \multicolumn{3}{c}{Probabilities} & \multicolumn{2}{|c}{Probabilities} \\
\multicolumn{1}{c}{Insurer} & & \multicolumn{1}{c}{Standard} &	\multicolumn{1}{|c}{Profits$\geq$10\%} & Profits$\geq$5\% & Profits$\geq$0\% &  \multicolumn{1}{c}{Losses$\leq$5\%} & Losses$\leq$10\% \\
\multicolumn{1}{c}{Size} & \multicolumn{1}{c}{Premiums} & \multicolumn{1}{c}{Error} & \multicolumn{1}{|c}{P=0.5000} & P=0.8413 & P=0.9772 & \multicolumn{1}{c}{P=0.9987} & P=1.0000 \\
\hline
309,000,000	&	1,236,000,000,000	&	0.002844	&	0.7500	&	0.7972	&	0.8443	&	0.8915	&	0.9386	\\
300,000,000	&	1,200,000,000,000	&	0.002887	&	0.7500	&	0.7971	&	0.8442	&	0.8913	&	0.9385	\\
250,000,000	&	1,000,000,000,000	&	0.003162	&	0.7500	&	0.7968	&	0.8437	&	0.8905	&	0.9374	\\
200,000,000	&	800,000,000,000	&	0.003536	&	0.7500	&	0.7965	&	0.8429	&	0.8894	&	0.9359	\\
150,000,000	&	600,000,000,000	&	0.004082	&	0.7500	&	0.7959	&	0.8418	&	0.8878	&	0.9337	\\
100,000,000	&	400,000,000,000	&	0.005000	&	0.7500	&	0.7950	&	0.8400	&	0.8850	&	0.9300	\\
50,000,000	&	200,000,000,000	&	0.007071	&	0.7500	&	0.7929	&	0.8359	&	0.8788	&	0.9217	\\
40,000,000	&	160,000,000,000	&	0.007906	&	0.7500	&	0.7921	&	0.8342	&	0.8763	&	0.9184	\\
30,000,000	&	120,000,000,000	&	0.009129	&	0.7500	&	0.7909	&	0.8317	&	0.8726	&	0.9135	\\
20,000,000	&	80,000,000,000	&	0.011180	&	0.7500	&	0.7888	&	0.8276	&	0.8665	&	0.9053	\\
10,000,000	&	40,000,000,000	&	0.015811	&	0.7500	&	0.7842	&	0.8184	&	0.8526	&	0.8868	\\
1,000,000	&	4,000,000,000	&	0.050000	&	0.7500	&	0.7500	&	0.7500	&	0.7500	&	0.7500	\\
900,000	&	3,600,000,000	&	0.052705	&	0.7500	&	0.7473	&	0.7446	&	0.7419	&	0.7392	\\
800,000	&	3,200,000,000	&	0.055902	&	0.7500	&	0.7441	&	0.7382	&	0.7323	&	0.7264	\\
700,000	&	2,800,000,000	&	0.059761	&	0.7500	&	0.7402	&	0.7305	&	0.7207	&	0.7110	\\
600,000	&	2,400,000,000	&	0.064550	&	0.7500	&	0.7355	&	0.7209	&	0.7064	&	0.6918	\\
500,000	&	2,000,000,000	&	0.070711	&	0.7500	&	0.7293	&	0.7086	&	0.6879	&	0.6672	\\
400,000	&	1,600,000,000	&	0.079057	&	0.7500	&	0.7209	&	0.6919	&	0.6628	&	0.6338	\\
300,000	&	1,200,000,000	&	0.091287	&	0.7500	&	0.7087	&	0.6674	&	0.6261	&	0.5849	\\
200,000	&	800,000,000	&	0.111803	&	0.7500	&	0.6882	&	0.6264	&	0.5646	&	0.5028	\\
100,000	&	400,000,000	&	0.158114	&	0.7500	&	0.6419	&	0.5338	&	0.4257	&	0.3175	\\
90,000	&	360,000,000	&	0.166667	&	0.7500	&	0.6333	&	0.5167	&	0.4000	&	0.2833	\\
80,000	&	320,000,000	&	0.176777	&	0.7500	&	0.6232	&	0.4964	&	0.3697	&	0.2429	\\
70,000	&	280,000,000	&	0.188982	&	0.7500	&	0.6110	&	0.4720	&	0.3331	&	0.1941	\\
60,000	&	240,000,000	&	0.204124	&	0.7500	&	0.5959	&	0.4418	&	0.2876	&	0.1335	\\
50,000	&	200,000,000	&	0.223607	&	0.7500	&	0.5764	&	0.4028	&	0.2292	&	0.0556	\\
40,000	&	160,000,000	&	0.250000	&	0.7500	&	0.5500	&	0.3500	&	0.1500	&	0.0000	\\
30,000	&	120,000,000	&	0.288675	&	0.7500	&	0.5113	&	0.2726	&	0.0340	&	0.0000	\\
20,000	&	80,000,000	&	0.353553	&	0.7500	&	0.4464	&	0.1429	&	0.0000	&	0.0000	\\
10,000	&	40,000,000	&	0.500000	&	0.7500	&	0.3000	&	0.0000	&	0.0000	&	0.0000	\\
5,000	&	20,000,000	&	0.707107	&	0.7500	&	0.0929	&	0.0000	&	0.0000	&	0.0000	\\
1,000	&	4,000,000	&	1.581139	&	0.7500	&	0.0000	&	0.0000	&	0.0000	&	0.0000	\\
100	&	400,000	&	5.000000	&	0.7500	&	0.0000	&	0.0000	&	0.0000	&	0.0000	\\
10	&	40,000	&	15.811388	&	0.7500	&	0.0000	&	0.0000	&	0.0000	&	0.0000	\\
1	&	4,000	&	50.000000	&	0.7500	&	0.0000	&	0.0000	&	0.0000	&	0.0000	\\
\hline
\end{tabular}\label{tab:MaximumSustainableBenefitsPercentOfPremiums}
}
\end{center}
Notes: MSBs of 0.0000 mean insurers cannot sustain positive MSBs throughout the year. These insurers can offer benefits sporadically, or close to year end, but not consistently throughout the year.\\
Prob[PI's Profits $\geq$ 5\%] = 0.84134 $ \Longrightarrow$ $MSB_N$ = 0.8000 - 1 * $\sigma_{e_{N}}$ \\
Prob[PI's Profits $\geq$ 0\%] = 0.9772 $\Longrightarrow$ $MSB_N$ = 0.8500 - 2 * $\sigma_{e_{N}}$ \\  
Prob[PI's Losses $\leq$ 5\%] = 0.9987 $\Longrightarrow$ $MSB_N$ = 0.9000 - 3 * $\sigma_{e_{N}}$ \\  
Prob[PI's Losses $\leq$ 10\%] = 0.99997 $\Longrightarrow$ $MSB_N$ = 0.9500 - 4 * $\sigma_{e_{N}}$ \\  
\end{table}


\newpage
\begin{table}[htbp]
%\vspace{-1in}
\caption{Dollar Value Of Sustainable Benefits While Matching PI's Probability Of Earning Profits (Avoiding Losses) By Portfolio Size} 
\begin{center}
\scalebox{0.8}{
\begin{tabular}{rrc|rrr|rr}
%\multicolumn{2}{c}{Genotype} & &
%\multicolumn{1}{c}{Dummy for additivity} &
%\multicolumn{1}{c}{Dummy for dominance }\\
%\multicolumn{1}{c}{Label} &    
%\multicolumn{1}{c}{Index i} &
%\multicolumn{1}{c}{Genotypic value ($\eta$)}&
%\multicolumn{1}{c}{effect $\alpha$ (x)} &
%\multicolumn{1}{c}{effect $\delta$ (z)}\\
\hline
\hline
& & & \multicolumn{3}{c}{Match PI's Profit} & \multicolumn{2}{|c}{Match PI's Loss Avoidance} \\
& & & \multicolumn{3}{c}{Probabilities} & \multicolumn{2}{|c}{Probabilities} \\
\multicolumn{1}{c}{Insurer} & & \multicolumn{1}{c}{Standard} &	\multicolumn{1}{|c}{Profits$\geq$10\%} & Profits$\geq$5\% & Profits$\geq$0\% &  \multicolumn{1}{c}{Losses$\leq$5\%} & Losses$\leq$10\% \\
\multicolumn{1}{c}{Size} & \multicolumn{1}{c}{Premiums} & \multicolumn{1}{c}{Error} & \multicolumn{1}{|c}{P=0.5000} & P=0.8413 & P=0.9772 & \multicolumn{1}{c}{P=0.9987} & P=1.0000 \\
\hline
309,000,000	&	1,236,000,000,000	&	0.002844	&	\$3,000	&	\$3,189	&	\$3,377	&	\$3,566	&	\$3,754	\\
300,000,000	&	1,200,000,000,000	&	0.002887	&	\$3,000	&	\$3,188	&	\$3,377	&	\$3,565	&	\$3,754	\\
250,000,000	&	1,000,000,000,000	&	0.003162	&	\$3,000	&	\$3,187	&	\$3,375	&	\$3,562	&	\$3,749	\\
200,000,000	&	800,000,000,000	&	0.003536	&	\$3,000	&	\$3,186	&	\$3,372	&	\$3,558	&	\$3,743	\\
150,000,000	&	600,000,000,000	&	0.004082	&	\$3,000	&	\$3,184	&	\$3,367	&	\$3,551	&	\$3,735	\\
100,000,000	&	400,000,000,000	&	0.005000	&	\$3,000	&	\$3,180	&	\$3,360	&	\$3,540	&	\$3,720	\\
50,000,000	&	200,000,000,000	&	0.007071	&	\$3,000	&	\$3,172	&	\$3,343	&	\$3,515	&	\$3,687	\\
40,000,000	&	160,000,000,000	&	0.007906	&	\$3,000	&	\$3,168	&	\$3,337	&	\$3,505	&	\$3,674	\\
30,000,000	&	120,000,000,000	&	0.009129	&	\$3,000	&	\$3,163	&	\$3,327	&	\$3,490	&	\$3,654	\\
20,000,000	&	80,000,000,000	&	0.011180	&	\$3,000	&	\$3,155	&	\$3,311	&	\$3,466	&	\$3,621	\\
10,000,000	&	40,000,000,000	&	0.015811	&	\$3,000	&	\$3,137	&	\$3,274	&	\$3,410	&	\$3,547	\\
1,000,000	&	4,000,000,000	&	0.050000	&	\$3,000	&	\$3,000	&	\$3,000	&	\$3,000	&	\$3,000	\\
900,000	&	3,600,000,000	&	0.052705	&	\$3,000	&	\$2,989	&	\$2,978	&	\$2,968	&	\$2,957	\\
800,000	&	3,200,000,000	&	0.055902	&	\$3,000	&	\$2,976	&	\$2,953	&	\$2,929	&	\$2,906	\\
700,000	&	2,800,000,000	&	0.059761	&	\$3,000	&	\$2,961	&	\$2,922	&	\$2,883	&	\$2,844	\\
600,000	&	2,400,000,000	&	0.064550	&	\$3,000	&	\$2,942	&	\$2,884	&	\$2,825	&	\$2,767	\\
500,000	&	2,000,000,000	&	0.070711	&	\$3,000	&	\$2,917	&	\$2,834	&	\$2,751	&	\$2,669	\\
400,000	&	1,600,000,000	&	0.079057	&	\$3,000	&	\$2,884	&	\$2,768	&	\$2,651	&	\$2,535	\\
300,000	&	1,200,000,000	&	0.091287	&	\$3,000	&	\$2,835	&	\$2,670	&	\$2,505	&	\$2,339	\\
200,000	&	800,000,000	&	0.111803	&	\$3,000	&	\$2,753	&	\$2,506	&	\$2,258	&	\$2,011	\\
100,000	&	400,000,000	&	0.158114	&	\$3,000	&	\$2,568	&	\$2,135	&	\$1,703	&	\$1,270	\\
90,000	&	360,000,000	&	0.166667	&	\$3,000	&	\$2,533	&	\$2,067	&	\$1,600	&	\$1,133	\\
80,000	&	320,000,000	&	0.176777	&	\$3,000	&	\$2,493	&	\$1,986	&	\$1,479	&	\$972	\\
70,000	&	280,000,000	&	0.188982	&	\$3,000	&	\$2,444	&	\$1,888	&	\$1,332	&	\$776	\\
60,000	&	240,000,000	&	0.204124	&	\$3,000	&	\$2,384	&	\$1,767	&	\$1,151	&	\$534	\\
50,000	&	200,000,000	&	0.223607	&	\$3,000	&	\$2,306	&	\$1,611	&	\$917	&	\$222	\\
40,000	&	160,000,000	&	0.250000	&	\$3,000	&	\$2,200	&	\$1,400	&	\$600	&	\$0	\\
30,000	&	120,000,000	&	0.288675	&	\$3,000	&	\$2,045	&	\$1,091	&	\$136	&	\$0	\\
20,000	&	80,000,000	&	0.353553	&	\$3,000	&	\$1,786	&	\$572	&	\$0	&	\$0	\\
10,000	&	40,000,000	&	0.500000	&	\$3,000	&	\$1,200	&	\$0	&	\$0	&	\$0	\\
5,000	&	20,000,000	&	0.707107	&	\$3,000	&	\$372	&	\$0	&	\$0	&	\$0	\\
1,000	&	4,000,000	&	1.581139	&	\$3,000	&	\$0	&	\$0	&	\$0	&	\$0	\\
100	&	400,000	&	5.000000	&	\$3,000	&	\$0	&	\$0	&	\$0	&	\$0	\\
10	&	40,000	&	15.811388	&	\$3,000	&	\$0	&	\$0	&	\$0	&	\$0	\\
1	&	4,000	&	50.000000	&	\$3,000	&	\$0	&	\$0	&	\$0	&	\$0	\\
\hline
\end{tabular}\label{tab:MaximumSustainableBenefitInDollars}
}
\end{center}
Notes: Benefit levels of \$0 mean insurers cannot sustain any positive level of benefits throughout the year. These insurers can offer benefits sporadically, or close to year end, but not consistently throughout the year.\\
Prob[PI's Profits $\geq$ 5\%] = 0.84134 $\Longrightarrow$ Dollar Benefits = \$4,000 * (0.8000 - 1 * $\sigma_{e_{N}}$) \\
Prob[PI's Profits $\geq$ 0\%] = 0.9772 $\Longrightarrow$ Dollar Benefits = \$4,000 * (0.8500 - 2 * $\sigma_{e_{N}}$) \\
Prob[PI's Losses $\leq$ 5\%] = 0.9987 $\Longrightarrow$ Dollar Benefits = \$4,000 * (0.9000 - 3 * $\sigma_{e_{N}}$) \\
Prob[PI's Losses $\leq$ 10\%] = 0.99997 $\Longrightarrow$ Dollar Benefits = \$4,000 * (0.9500 - 4 * $\sigma_{e_{N}}$) \\  
\end{table}
